I'll preface this by saying that I am not debating whenever this is good or bad.

The point here is to make car ownership inconvenient and unaffordable so any implication that it encourages more driving is false by default as there will be less cars on the road to begin with.

I think both you and parent can easily be correct simultaneously. It is possible for both of these things to be true: there being less cars on the road and people who are in the remainder of cars on the road driving more than they would normally had the taxes been lower.

Whether the latter offsets the former to a significant margin appears to be the matter of debate implied here.